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<div  id='write'  class = 'is-mac first-line-indent'><h2><a name="高等数学计划·0312--📖" class="md-header-anchor"></a><span>高等数学计划·0312  📖：</span></h2><h4><a name="函数和映射基本初等函数）" class="md-header-anchor"></a><span>函数和映射（基本初等函数）：</span></h4><h5><a name="甩图" class="md-header-anchor"></a><span>甩图：</span></h5><p><img src="1.1_2.png" alt="img" style="zoom:50%;" /></p><h5><a name="课后习题" class="md-header-anchor"></a><span>课后习题：</span></h5><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n10" cid="n10" mdtype="math_block">
			
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x="11610" y="0"></use><use xlink:href="#E8-MJMAIN-2B" x="12055" y="0"></use><use xlink:href="#E8-MJMAIN-221E" x="12833" y="0"></use><use xlink:href="#E8-MJMAIN-29" x="13833" y="0"></use><g transform="translate(14222,0)"><text font-family="STIXGeneral,'Arial Unicode MS',serif" stroke="none" transform="scale(48.742) matrix(1 0 0 -1 0 0)">，</text></g><use xlink:href="#E8-MJMATHI-72" x="14899" y="0"></use><use xlink:href="#E8-MJMATHI-61" x="15350" y="0"></use><use xlink:href="#E8-MJMATHI-6E" x="15879" y="0"></use><use xlink:href="#E8-MJMATHI-67" x="16479" y="0"></use><use xlink:href="#E8-MJMATHI-65" x="16959" y="0"></use><g transform="translate(17425,0)"><text font-family="STIXGeneral,'Arial Unicode MS',serif" stroke="none" transform="scale(48.742) matrix(1 0 0 -1 0 0)">：</text></g><use xlink:href="#E8-MJMAIN-28" x="18102" y="0"></use><use xlink:href="#E8-MJMAIN-2212" x="18491" y="0"></use><use xlink:href="#E8-MJMATHI-3C0" x="19269" y="0"></use><use xlink:href="#E8-MJMAIN-2F" x="19839" y="0"></use><use xlink:href="#E8-MJMAIN-32" x="20339" y="0"></use><use xlink:href="#E8-MJMAIN-2C" x="20839" y="0"></use><use xlink:href="#E8-MJMATHI-3C0" x="21284" y="0"></use><use xlink:href="#E8-MJMAIN-2F" x="21854" y="0"></use><use xlink:href="#E8-MJMAIN-32" x="22354" y="0"></use><use xlink:href="#E8-MJMAIN-29" x="22854" y="0"></use></g><g transform="translate(0,-4467)"><use xlink:href="#E8-MJMATHI-79" x="0" y="0"></use><use xlink:href="#E8-MJMAIN-3D" x="774" y="0"></use><use xlink:href="#E8-MJMATHI-73" x="1830" y="0"></use><use xlink:href="#E8-MJMATHI-69" x="2299" y="0"></use><use xlink:href="#E8-MJMATHI-6E" x="2644" y="0"></use><use xlink:href="#E8-MJMATHI-61" x="3244" y="0"></use><use xlink:href="#E8-MJMATHI-72" x="3773" y="0"></use><use xlink:href="#E8-MJMATHI-63" x="4224" y="0"></use><use xlink:href="#E8-MJMATHI-73" x="4657" y="0"></use><use xlink:href="#E8-MJMATHI-69" x="5126" y="0"></use><use xlink:href="#E8-MJMATHI-6E" x="5471" y="0"></use><use xlink:href="#E8-MJMAIN-28" x="6071" y="0"></use><use xlink:href="#E8-MJMATHI-78" x="6460" y="0"></use><use xlink:href="#E8-MJMAIN-29" x="7032" y="0"></use><use xlink:href="#E8-MJMAIN-3D" x="7699" y="0"></use><use xlink:href="#E8-MJMATHI-78" x="8755" y="0"></use><use xlink:href="#E8-MJMAIN-2C" x="9327" y="0"></use><use xlink:href="#E8-MJMATHI-64" x="9771" y="0"></use><use xlink:href="#E8-MJMATHI-6F" x="10294" y="0"></use><use xlink:href="#E8-MJMATHI-6D" x="10779" y="0"></use><use xlink:href="#E8-MJMATHI-61" x="11657" y="0"></use><use xlink:href="#E8-MJMATHI-69" x="12186" y="0"></use><use xlink:href="#E8-MJMATHI-6E" x="12531" y="0"></use><g transform="translate(13131,0)"><text font-family="STIXGeneral,'Arial Unicode MS',serif" stroke="none" transform="scale(48.742) matrix(1 0 0 -1 0 0)">：</text></g><use xlink:href="#E8-MJMAIN-5B" x="13808" y="0"></use><use xlink:href="#E8-MJMAIN-2212" x="14086" y="0"></use><use xlink:href="#E8-MJMAIN-31" x="14864" y="0"></use><use xlink:href="#E8-MJMAIN-2C" x="15364" y="0"></use><use xlink:href="#E8-MJMAIN-31" x="15809" y="0"></use><use xlink:href="#E8-MJMAIN-5D" x="16309" y="0"></use><use xlink:href="#E8-MJMAIN-2C" x="16587" y="0"></use><use xlink:href="#E8-MJMATHI-72" x="17032" y="0"></use><use xlink:href="#E8-MJMATHI-61" x="17483" y="0"></use><use xlink:href="#E8-MJMATHI-6E" x="18012" y="0"></use><use xlink:href="#E8-MJMATHI-67" x="18612" y="0"></use><use xlink:href="#E8-MJMATHI-65" x="19092" y="0"></use><g transform="translate(19558,0)"><text font-family="STIXGeneral,'Arial Unicode MS',serif" stroke="none" transform="scale(48.742) matrix(1 0 0 -1 0 0)">：</text></g><use xlink:href="#E8-MJMAIN-5B" x="20235" y="0"></use><use xlink:href="#E8-MJMAIN-2212" x="20513" y="0"></use><use xlink:href="#E8-MJMATHI-3C0" x="21291" y="0"></use><use xlink:href="#E8-MJMAIN-2F" x="21861" y="0"></use><use xlink:href="#E8-MJMAIN-32" x="22361" y="0"></use><use xlink:href="#E8-MJMAIN-2C" x="22861" y="0"></use><use xlink:href="#E8-MJMATHI-3C0" x="23305" y="0"></use><use xlink:href="#E8-MJMAIN-2F" x="23875" y="0"></use><use xlink:href="#E8-MJMAIN-32" x="24375" y="0"></use><use xlink:href="#E8-MJMAIN-5D" x="24875" y="0"></use></g></g></svg></span><script type="math/tex">y＝arcsin(x)，domain：[-1,1] ，range：[-π/2,π/2]\\y=arccos(x)domain：[-1,1] ，range：[0,π]
\\y=arctan(x)domain(-∞,+∞)，range：(-π/2,π/2)
\\y=sinarcsin(x)=x,domain：[-1,1],range：[-π/2,π/2]</script></p><p><span>上述题解：</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n13" cid="n13" mdtype="math_block">
			
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y="0"></use><use xlink:href="#E2-MJMAIN-29" x="13018" y="0"></use></g></g></g></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-2">\begin{align*}
&1:\ 3x+2 \geqslant 0 \to \ x \geqslant-\frac{2}{3},result：\left[-\frac{2}{3},+\infty\right)\\
&2:1-x^{2} \neq 0 \Rightarrow x \neq \pm 1 ，result：(-\infty,-1) \cup(-1,1) \cup(1,+\infty)
\\&3:1-x^{2} \geqslant 0 \Rightarrow x \neq 0 \to[-1,0) \cup(0,1]
\\&4:4-x^{2}>0 \to|x|<2  \to\ result:(-2,2)
\\&5:x\geqslant0 
\\&6:x+1 \neq k \pi+\frac{\pi}{2}(k \in \mathbf{Z}) \to (tan)
\\&7:for \ this\  case:|x-3| \leqslant 1 \Rightarrow 2 \leqslant x \leqslant 4
\\&8:3-x \geqslant 0 \text { H. } x \neq 0\to(-\infty, 0) \cup(0,3]
\\&9:x+1>0 \Rightarrow x>-1\to(-1,+\infty)
\\&0:x \neq 0\to(-\infty, 0) \cup(0,+\infty)
\end{align*}</script></div></div><p><span>另外，求解函数是否相等的问题，以两大角度切入，对应法则和定义域，function和domain同时满足相等，才可以定义为两个函数相等。</span></p><p><span>2.求解以下函数单调性，区间固定。</span></p><p><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="54.363ex" height="3.179ex" viewBox="0 -928.1 23406.3 1368.8" role="img" focusable="false" style="vertical-align: -1.024ex;"><defs><path stroke-width="0" id="E9-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path stroke-width="0" id="E9-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 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xlink:href="#E11-MJMAIN-6C"></use><use xlink:href="#E11-MJMAIN-6E" x="278" y="0"></use></g><g transform="translate(24030,0)"><g transform="translate(286,0)"><rect stroke="none" width="845" height="60" x="0" y="220"></rect><g transform="translate(60,507)"><use transform="scale(0.707)" xlink:href="#E11-MJMATHI-78" x="0" y="0"></use><use transform="scale(0.5)" xlink:href="#E11-MJMAIN-32" x="808" y="-213"></use></g><g transform="translate(60,-345)"><use transform="scale(0.707)" xlink:href="#E11-MJMATHI-78" x="0" y="0"></use><use transform="scale(0.5)" xlink:href="#E11-MJMAIN-31" x="808" y="-213"></use></g></g></g><use xlink:href="#E11-MJMAIN-3E" x="25560" y="0"></use><use xlink:href="#E11-MJMAIN-30" x="26616" y="0"></use></g></g></svg></span><script type="math/tex">x_1-x_2 >0 \\ ln \ image \ get \ \ln(x_2)<ln(x_1) \\f\left(x_{2}\right)-f\left(x_{1}\right)=x_{2}+\ln x_{2}-x_{1}-\ln x_{1}=x_{2}-x_{1}+\ln \frac{x_{2}}{x_{1}}>0</script></p><p><span>答案是单调递增。</span></p><p><span>5.奇函数定义可得</span></p><h5><a name="反函数求法" class="md-header-anchor"></a><span>反函数求法：</span></h5><p><span>通过一个</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="11.515ex" height="2.839ex" viewBox="0 -928.1 4958 1222.5" role="img" focusable="false" style="vertical-align: -0.684ex;"><defs><path stroke-width="0" id="E12-MJMATHI-79" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path stroke-width="0" id="E12-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path stroke-width="0" id="E12-MJMATHI-78" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path stroke-width="0" id="E12-MJMAIN-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path stroke-width="0" id="E12-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="0" id="E12-MJMAIN-221A" d="M95 178Q89 178 81 186T72 200T103 230T169 280T207 309Q209 311 212 311H213Q219 311 227 294T281 177Q300 134 312 108L397 -77Q398 -77 501 136T707 565T814 786Q820 800 834 800Q841 800 846 794T853 782V776L620 293L385 -193Q381 -200 366 -200Q357 -200 354 -197Q352 -195 256 15L160 225L144 214Q129 202 113 190T95 178Z"></path><path stroke-width="0" id="E12-MJMAIN-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E12-MJMATHI-79" x="0" y="0"></use><use xlink:href="#E12-MJMAIN-3D" x="774" y="0"></use><g transform="translate(1830,0)"><use transform="scale(0.5)" xlink:href="#E12-MJMAIN-33" x="625" y="918"></use><use xlink:href="#E12-MJMAIN-221A" x="0" y="14"></use><rect stroke="none" width="2294" height="60" x="833" y="754"></rect><g transform="translate(833,0)"><use xlink:href="#E12-MJMATHI-78" x="0" y="0"></use><use xlink:href="#E12-MJMAIN-2B" x="794" y="0"></use><use xlink:href="#E12-MJMAIN-31" x="1794" y="0"></use></g></g></g></svg></span><script type="math/tex">y=\sqrt[3]{x+1}</script><span>去解得</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n85" cid="n85" mdtype="math_block">
			
		<div class="md-rawblock-container md-math-container" tabindex="-1"><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-3-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="10.639ex" height="2.953ex" viewBox="0 -976.8 4580.7 1271.3" role="img" focusable="false" style="vertical-align: -0.684ex; max-width: 100%;"><defs><path stroke-width="0" id="E3-MJMATHI-78" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path stroke-width="0" id="E3-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path stroke-width="0" id="E3-MJMATHI-79" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path stroke-width="0" id="E3-MJMAIN-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path><path stroke-width="0" id="E3-MJMAIN-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path stroke-width="0" id="E3-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E3-MJMATHI-78" x="0" y="0"></use><use xlink:href="#E3-MJMAIN-3D" x="849" y="0"></use><g transform="translate(1905,0)"><use xlink:href="#E3-MJMATHI-79" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E3-MJMAIN-33" x="705" y="583"></use></g><use xlink:href="#E3-MJMAIN-2212" x="3080" y="0"></use><use xlink:href="#E3-MJMAIN-31" x="4080" y="0"></use></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-3">x=y^{3}-1</script></div></div><p><span>得到的就是</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.154ex" height="1.934ex" viewBox="0 -538.2 497 832.6" role="img" focusable="false" style="vertical-align: -0.684ex;"><defs><path stroke-width="0" id="E13-MJMATHI-79" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E13-MJMATHI-79" x="0" y="0"></use></g></svg></span><script type="math/tex">y</script><span>的反函数。</span></p><p><span>11.复合函数求解，不再赘述。</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n93" cid="n93" mdtype="math_block">
			
		<div class="md-rawblock-container md-math-container" tabindex="-1"><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-4-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="39.572ex" height="17.217ex" viewBox="0 -3950.1 17037.9 7412.8" role="img" focusable="false" style="vertical-align: -8.042ex; max-width: 100%;"><defs><path stroke-width="0" id="E4-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path stroke-width="0" id="E4-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="0" id="E4-MJMAIN-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path><path stroke-width="0" id="E4-MJMATHI-79" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path stroke-width="0" id="E4-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path stroke-width="0" id="E4-MJMATHI-75" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 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321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path stroke-width="0" id="E4-MJMAIN-69" d="M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 549 87 564T69 609ZM247 0Q232 3 143 3Q132 3 106 3T56 1L34 0H26V46H42Q70 46 91 49Q100 53 102 60T104 102V205V293Q104 345 102 359T88 378Q74 385 41 385H30V408Q30 431 32 431L42 432Q52 433 70 434T106 436Q123 437 142 438T171 441T182 442H185V62Q190 52 197 50T232 46H255V0H247Z"></path><path stroke-width="0" id="E4-MJMAIN-6E" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z"></path><path stroke-width="0" id="E4-MJMATHI-78" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path stroke-width="0" id="E4-MJMATHI-3C0" d="M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z"></path><path stroke-width="0" id="E4-MJMAIN-36" d="M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 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transform="translate(11251,0)"><use xlink:href="#E5-MJMAIN-65" x="0" y="0"></use><g transform="translate(444,362)"><use transform="scale(0.707)" xlink:href="#E5-MJMAIN-2212" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E5-MJMAIN-32" x="778" y="0"></use></g></g></g></g></g></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-5">(1) y=\sin ^{2} x, y_{1}=\frac{1}{4}, y_{2}=\frac{3}{4}\begin{array}{l}\text { (2) } y=\sin 2 x, y_{1}=\frac{\sqrt{2}}{2}, y_{2}=1 \\ \text { (3) } y=\sqrt{1+x^{2}}, y_{1}=\sqrt{2}, y_{2}=\sqrt{5} \\ \text { (4) } y=\mathrm{e}^{x^{2}}, y_{1}=1, y_{2}=\mathrm{e} \\ \text { (5) } y=\mathrm{e}^{2 x}, y_{1}=\mathrm{e}^{2}, y_{2}=\mathrm{e}^{-2}\end{array}</script></div></div><h5><a name="下一节数列的极限" class="md-header-anchor"></a><span>下一节：数列的极限   </span></h5><h2><a name="🏃" class="md-header-anchor"></a><span>🏃</span></h2><p>&nbsp;</p></div>
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